A common foodstuff is found to contain .00125% iron. The serving size is
87.0 grams. If the recommended daily allowance is 18mg of iron, how many
servings would a person have to eat to get 100% of the daily allowance of
iron?

For a particular job, Moe should get 40% of the gross pay, Larry
should get 30%, and Curly should get 30%, assuming they all work the
same number of hours. But how should the money be divided if they
work different numbers of hours?

What amounts of 9 percent and 12 percent alcohol do you mix to get
300,000 gallons of 10 percent alcohol? For each 5-cent increase in the
monthly subscription price, 4 people will decide not to subscribe to
cable TV...

In an auditorium, the ratio of the number of girls to the number of
boys was 5:9. When 203 girls entered the auditorium, the new ratio of
the number of girls to the number of boys became 4:3. How many pupils
were in the auditorium at first?

Doctor Wallace extends the kind of proportional thinking suggested by a student
attempting a problem that Abraham Lincoln once solved.
Doctor Peterson follows up by looking back into the kind of ciphering textbooks the
Civil War President would have learned from, then solves the same interest rate problem with a
formula more familiar to modern students.

A student who knows facts about populations and physical chemistry struggles to
determine how long would it take the world to consume a mole of Skittles. Doctor Ian
shows the power of algebra by introducing a key assumption that makes this Fermi
problem approachable.

A student solves a problem about combined rates of work, but struggles to
understand "units of work per man-hour" and the other ratios it entails. Doctor Ian
approaches the problem first by simplifying it into unit rates, then distinguishes the
direct proportions from the inverse ones en route to a general template that would
model the combination of any work rates.

An adult wonders how to logically reason through problems that entail combining rates of work. Moved to re-examine the mechanics he learned in high school, Doctor Jerry introduces a
constant tacitly assumed in the wording of such problems.